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To overcome computational bottlenecks of various data perturbation procedures such as the bootstrap and cross-validations, we propose the Generative Multi-purpose Sampler (GMS), which directly constructs a generator function to produce solutions of weighted M-estimators from a set of given weights and tuning parameters. The GMS is implemented by a single optimization procedure without having to repeatedly evaluate the minimizers of weighted losses, and is thus capable of significantly reducing the computational time. We demonstrate that the GMS framework enables the implementation of various statistical procedures that would be unfeasible in a conventional framework, such as iterated bootstrap procedures and cross-validation for penalized likelihood. To construct a computationally efficient generator function, we also propose a novel form of neural network called the weight multiplicative multilayer perceptron to achieve fast convergence. An R package called GMS is provided, which runs under Pytorch to implement the proposed methods and allows the user to provide a customized loss function to tailor to their own models of interest. for this article are available online. [ABSTRACT FROM AUTHOR]

AbstractQuantile regression and conditional density estimation can reveal structure that is missed by mean regression, such as multimodality and skewness. In this article, we introduce a deep learning generative model for joint quantile estimation called Penalized Generative Quantile Regression (PGQR). Our approach simultaneously generates samples from many random quantile levels, allowing us to infer the conditional distribution of a response variable given a set of covariates. Our method employs a novel variability penalty to avoid the problem of vanishing variability, or memorization, in deep generative models. Further, we introduce a new family of partial monotonic neural networks (PMNN) to circumvent the problem of crossing quantile curves. A major benefit of PGQR is that it can be fit using a single optimization, thus, bypassing the need to repeatedly train the model at multiple quantile levels or use computationally expensive cross-validation to tune the penalty parameter. We illustrate the efficacy of PGQR through extensive simulation studies and analysis of real datasets. Code to implement our method is available at https://github.com/shijiew97/PGQR. [ABSTRACT FROM AUTHOR]

Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficulties in both computations and flexibilities of prior choices. To ease these challenges, we propose the neuronized priors to unify and extend some popular shrinkage priors, such as Laplace, Cauchy, horseshoe, and spike-and-slab priors. A neuronized prior can be written as the product of a Gaussian weight variable and a scale variable transformed from Gaussian via an activation function. Compared with classic spike-and-slab priors, the neuronized priors achieve the same explicit variable selection without employing any latent indicator variables, which results in both more efficient and flexible posterior sampling and more effective posterior modal estimation. Theoretically, we provide specific conditions on the neuronized formulation to achieve the optimal posterior contraction rate, and show that a broadly applicable MCMC algorithm achieves an exponentially fast convergence rate under the neuronized formulation. We also examine various simulated and real data examples and demonstrate that using the neuronization representation is computationally more or comparably efficient than its standard counterpart in all well-known cases. An R package NPrior is provided for using neuronized priors in Bayesian linear regression. [ABSTRACT FROM AUTHOR]

Longitudinal item response data are common in social science, educational science, and psychology, among other disciplines. Studying the time-varying relationships between items is crucial for educational assessment or designing marketing strategies from survey questions. Although dynamic network models have been widely developed, we cannot apply them directly to item response data because there are multiple systems of nodes with various types of local interactions among items, resulting in multiplex network structures. We propose a new model to study these temporal interactions among items by embedding the functional parameters within the exponential random graph model framework. Inference on such models is difficult because the likelihood functions contain intractable normalizing constants. Furthermore, the number of functional parameters grows exponentially as the number of items increases. Variable selection for such models is not trivial because standard shrinkage approaches do not consider temporal trends in functional parameters. To overcome these challenges, we develop a novel Bayes approach by combining an auxiliary variable MCMC algorithm and a recently developed functional shrinkage method. We apply our algorithm to survey and review datasets, illustrating that the proposed approach can avoid the evaluation of intractable normalizing constants as well as the detection of significant temporal interactions among items. Through a simulation study under different scenarios, we examine the performance of our algorithm. Our method is, to our knowledge, the first attempt to select functional variables for models with intractable normalizing constants. for this article are available online. [ABSTRACT FROM AUTHOR]

We introduce a new shrinkage prior on function spaces, called the functional horseshoe (fHS) prior, that encourages shrinkage toward parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity on model parameters. We study the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We also demonstrate consistency of the model selection procedure that thresholds the shrinkage parameter of the fHS prior. We apply the fHS prior to nonparametric additive models and compare its performance with procedures based on the standard horseshoe prior and several penalized likelihood approaches. We find that the new procedure achieves smaller estimation error and more accurate model selection than other procedures in several simulated and real examples. for this article, which contain additional simulated and real data examples, MCMC diagnostics, and proofs of the theoretical results, are available online. [ABSTRACT FROM AUTHOR]

Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain cannot cross energy barrier between modes due to the energy conservation property. In this paper, we propose a Stochastic Approximate Hamilton Monte Carlo (SAHMC) algorithm for generating samples from multimodal density under the Hamiltonian Monte Carlo (HMC) framework. SAHMC can adaptively lower the energy barrier to move the Hamiltonian trajectory more frequently and more easily between modes. Our simulation studies show that the potential for SAHMC to explore a multimodal target distribution is more efficient than HMC-based implementations. [ABSTRACT FROM AUTHOR]

Significant advances in biotechnology have allowed for simultaneous measurement of molecular data across multiple genomic, epigenomic and transcriptomic levels from a single tumor/patient sample. This has motivated systematic data-driven approaches to integrate multi-dimensional structured datasets, since cancer development and progression is driven by numerous co-ordinated molecular alterations and the interactions between them. We propose a novel multi-scale Bayesian approach that combines integrative graphical structure learning from multiple sources of data with a variable selection framework—to determine the key genomic drivers of cancer progression. The integrative structure learning is first accomplished through novel joint graphical models for heterogeneous (mixed scale) data, allowing for flexible and interpretable incorporation of prior existing knowledge. This subsequently informs a variable selection step to identify groups of co-ordinated molecular features within and across platforms associated with clinical outcomes of cancer progression, while according appropriate adjustments for multicollinearity and multiplicities. We evaluate our methods through rigorous simulations to establish superiority over existing methods that do not take the network and/or prior information into account. Our methods are motivated by and applied to a glioblastoma multiforme (GBM) dataset from The Cancer Genome Atlas to predict patient survival times integrating gene expression, copy number and methylation data. We find a high concordance between our selected prognostic gene network modules with known associations with GBM. In addition, our model discovers several novel cross-platform network interactions (both cis and trans acting) between gene expression, copy number variation associated gene dosing and epigenetic regulation through promoter methylation, some with known implications in the etiology of GBM. Our framework provides a useful tool for biomedical researchers, since clinical prediction using multi-platform genomic information is an important step towards personalized treatment of many cancers. [ABSTRACT FROM AUTHOR]

In this paper, we study the Kullback–Leibler (KL) information of a censored variable, which we will simply call itcensoredKL information. ThecensoredKL information is shown to have thenecessarymonotonicity property in addition to inherent properties of nonnegativity and characterization. We also present a representation of thecensoredKL information in terms of the relative risk and study its relation with the Fisher information in censored data. Finally, we evaluate the estimatedcensoredKL information as a goodness-of-fit test statistic. [ABSTRACT FROM PUBLISHER]

In this paper, a design procedure is proposed for networked control systems (NCSs) using an embedded real-time operating system (RTOS). In a conventional design of NCSs, well-designed control algorithms do not result in the intended control performance after an implementation because of time delays, such as network-induced delays and controller computation delays. The proposed design procedure shows how to minimize the degradation of the control performance caused by the time delays. A performance index (PI) is derived from the difference between the performance of a simulated system and the performance of an implemented system with time delays. By using the proposed PI, optimized periods and priorities of tasks and communication messages of NCSs were determined. The design procedure was verified by designing a networked traction control system (TCS) using a real-time operating system for automotive electronics, OSEK-OS. The designed TCS was realized and tested by using a rapid control prototyping platform and a hardware-in-the-loop simulation environment. [ABSTRACT FROM AUTHOR]

Rapid control prototyping (RCP) is one of the most important technologies for speeding up the development process of the electronic control unit ( ECU ) used in the automotive control system. However, one big drawback of the conventional RCP platform is the transfer from RCP to target ECU implementation. In this study, a new RCP platform is proposed that provides a consistent environment for both the RCP development stage and the target ECU implementation stage. In order to make the rapid prototyping controller as similar to a production ECU as possible, the prototyping system follows the strictly layered architecture of the production ECU and separates the automatically generated code of software from the hand code. Finally, the feasibility of the developed target-identical RCP platform is evaluated through an air-to-fuel ratio (AFR) control application. [ABSTRACT FROM AUTHOR]